Finite Group Databasebeta

← #14910360

Subgroups — #14910360

Order 2816.

712 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622527C212yesmaximal, complemented
2#13080300C212yesmaximal, complemented
3#13070726C212yesmaximal, complemented
4#13070668C212yesmaximal, complemented
5#13070555C212yesmaximal, complemented
6#13070526C212yesmaximal, complemented
7C4×D176C211yesmaximal, characteristic, complemented
8#13070449C211yesmaximal, characteristic, complemented
9C11×#2249C211yesmaximal, characteristic, complemented
10C2×#66972C2212yes—
11C2×D8×D11C2212yescomplemented
12#10623207—22no—
13C2×C11×Q32C2211yescharacteristic, complemented
14C2×C11×SD32C2212yescomplemented
15C2×C11×D16C2211yescharacteristic
16C11×#495C2212yescomplemented
17#10622801C2212yescomplemented
18C2×#66892C2212yescomplemented
19#10622785—22no—
20#10622782—22no—
21#10622770C2212yes—
22C2×#66890C2212yes—
23#10622670—22no—
24#10622527—28no—
25C2×D176C2211yescharacteristic
26C2×#66862C2212yescomplemented
27C4×D88C2212yescomplemented
28C8×D44C2211yescharacteristic
29C4×C11×C16C2211yescharacteristic, complemented
30#10622202C2212yescomplemented
31#10622200C2212yescomplemented
32#10622147C2212yescomplemented
33(C2×D11)⋊C16C2212yescomplemented
34#10622142C2211yescharacteristic, complemented
35C4⋊(C11⋊C16)C2211yescharacteristic, complemented
36C2×#4343—22no—
37C2×D4×D11—22no—
38C2×C11×Q16C2312yes—
39C2×C11×SD16—22no—
40C2×C11×D8C2312yes—
41C11×#124—22no—
42#66999—22no—
43C2×#4325—22no—
44#66991—22no—
45C2×#4323—22no—
46#66972—24no—
47#66972—42no—
48D8×D11—24no—
49D8×D11—42no—
50C2×D88C2312yes—
51C2×C8×D11C2312yes—
52#66937—42no—
53#66936—42no—
54#66935—42no—
55C22⋊C4×D11—42no—
56C4×D44—22no—
57C4×D44D411yescharacteristic
58C11×Q32—41no—
59C11×SD32—24no—
60C11×D16—41no—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C4×C8×C11C2311yescharacteristic
64#66899—22no—
65#66896—22no—
66#66892—24no—
67#66890—24no—
68#66885—22no—
69(C2×D11)⋊C8D412yes—
70#66882C2312yes—
71C2×C11⋊C16C2312yes—
72C4⋊(C11⋊C8)D411yescharacteristic
73D176D414yescomplemented
74#66862—24no—
75#33839—111nomaximal, Sylow
76C23×D11—42no—
77C2×Q8×C11—22no—
78C2×D4×C11—22no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81#4343—44no—
82#4343—82no—
83D4×D11—44no—
84D4×D11—82no—
85C2×D44—22no—
86C2×D44—42no—
87C2×D44D811yescharacteristic
88C2×C4×D11—42no—
89C2×C4×D11—42no—
90C2×C4×D11C2×D412yes—
91C11×Q16—22no—
92C11×Q16—22no—
93C11×SD16—82no—
94C11×D8—22no—
95C11×D8—22no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C42×C11C2×D411yescharacteristic
101C22⋊Dic11—42no—
102#4325—44no—
103#4323—44no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4D812yes—
107C4⋊Dic11—22no—
108C4⋊Dic11D811yescharacteristic
109Dic11⋊C4—42no—
110C2×C11⋊C8C2×D412yes—
111D88—22no—
112D88C2×D414yes—
113C8×D11—22no—
114C8×D11—22no—
115C11×C16—21no—
116C11×C16C2×D412yes—
117C11⋊C16—22no—
118C2×#509—112no—
119#3280—112no—
120#2249D1111yescharacteristic, complemented
121#2220—112no—
122#2210—112no—
123#2189—112no—
124#2184—112no—
125C4×D16—111no—
126#2169—111no—
127C23×C11—42no—
128C22×D11—42no—
129C22×D11—84no—
130C22×D11—84no—
131C22×D11—162no—
132C22×D11C2×D812yes—
133Q8×C11—42no—
134Q8×C11—42no—
135D4×C11—42no—
136D4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C22⋊D11—84no—
142C22⋊D11—162no—
143C2×Dic11—42no—
144C2×Dic11C2×D812yes—
145D44—24no—
146D44—41no—
147D44—42no—
148D44—84no—
149C4×D11—22no—
150C4×D11—22no—
151C4×D11—84no—
152C4×D11—162no—
153C8×C11—21no—
154C8×C11C22×D411yescharacteristic
155C8×C11H(5,𝔽2)11yescharacteristic
156C11⋊C8—22no—
157C2×#135—112no—
158C22×D8—112no—
159#546—222no—
160#509—228no—
161C2×Q32C2×D1111yescharacteristic, complemented
162C2×SD32—112no—
163C2×SD32C2×D1112yescomplemented
164C2×D16—112no—
165C2×D16—111no—
166C2×D16C2×D1111yescharacteristic
167C2×M32—112no—
168#495C2×D1112yescomplemented
169#467—112no—
170#466—112no—
171#463—222no—
172#450—222no—
173#449—222no—
174C4×D8—112no—
175C8×D4—111no—
176#366—111no—
177C4⋊C16—111no—
178#358—112no—
179#357—112no—
180#357—112no—
181C22⋊C16—112no—
182C4×C16C2×D1111yescharacteristic, complemented
183C22×C11—82no—
184C22×C11—82no—
185C22×C11—82no—
186C22×C11C22×D811yescharacteristic
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—44no—
191C2×D11—82no—
192C2×D11—82no—
193C2×D11—168no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—82no—
197C4×C11D4211yescharacteristic
198C4×C11#57611yescharacteristic
199Dic11—22no—
200Dic11—82no—
201C2×#41—222no—
202C22×D4—222no—
203#135—224no—
204#135—442no—
205C2×Q16C22×D1112yes—
206C2×SD16—22no—
207C2×SD16—222no—
208C2×D8—112no—
209C2×D8—222no—
210C2×D8—224no—
211C2×D8—442no—
212C2×D8C22×D1112yes—
213C22×C8—112no—
214#124—22no—
215#123—442no—
216C22⋊Q8—222no—
217#121—222no—
218#121—442no—
219#120—442no—
220C4×D4—111no—
221C4×D4—222no—
222C2×C22⋊C4—442no—
223Q32—41no—
224SD32—24no—
225SD32—224no—
226D16—41no—
227D16—114no—
228D16—224no—
229M32—224no—
230C2×C16—112no—
231C2×C16C22×D1111yescharacteristic
232C2×C16C22×D1111yescharacteristic
233#107—112no—
234C4⋊C8—111no—
235#103—222no—
236#102—222no—
237#102—222no—
238C22⋊C8—112no—
239C4×C8C22×D1111yescharacteristic
240C2×C11—162no—
241C2×C11D4×D811yescharacteristic
242C2×C11#341411yescharacteristic
243C2×C11#341511yescharacteristic
244D11—42no—
245D11—84no—
246C24—442no—
247#41—444no—
248#41—882no—
249C2×Q8—22no—
250C2×D4—22no—
251C2×D4—111no—
252C2×D4—222no—
253C2×D4—442no—
254C2×D4—442no—
255C2×D4—444no—
256C2×D4—442no—
257C2×D4—882no—
258C22×C4—112no—
259C22×C4—442no—
260C22×C4—442no—
261Q16—22no—
262Q16—22no—
263SD16—82no—
264SD16—444no—
265D8—22no—
266D8—22no—
267D8—114no—
268D8—222no—
269D8—444no—
270C2×C8—112no—
271C2×C8—222no—
272C2×C8—222no—
273C2×C8D4×D1111yescharacteristic
274C2×C8C23×D1111yescharacteristic
275C4⋊C4—111no—
276C4⋊C4—222no—
277C4⋊C4—442no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—112no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C42D4×D1111yescharacteristic
285C16—21no—
286C16—222no—
287C16D4×D1112yes—
288C11#3383911yescharacteristic, complemented, Sylow
289C23—42no—
290C23—112no—
291C23—442no—
292C23—884no—
293C23—884no—
294C23—1762no—
295Q8—42no—
296Q8—42no—
297D4—42no—
298D4—42no—
299D4—224no—
300D4—441no—
301D4—442no—
302D4—884no—
303D4—884no—
304D4—1762no—
305C2×C4—42no—
306C2×C4—112no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—442no—
310C2×C4—884no—
311C2×C4—1762no—
312C2×C4D8×D1111yescharacteristic
313C2×C4D8×D1111yescharacteristic
314C2×C4C2×D4×D1111yescharacteristic
315C8—21no—
316C8—222no—
317C8C2×D4×D1111yescharacteristic
318C8#6703711yescharacteristic
319C22—82no—
320C22—82no—
321C22—82no—
322C22—222no—
323C22—222no—
324C22—222no—
325C22—444no—
326C22—882no—
327C22—882no—
328C22—1768no—
329C22C2×D8×D1111yescharacteristic
330C4—21no—
331C4—21no—
332C4—82no—
333C4—222no—
334C4—882no—
335C4#1062324811yescharacteristic
336C4#1062328811yescharacteristic
337C2—162no—
338C2—442no—
339C2—884no—
340C2#1308029111yescharacteristic
341C2#1308174911yescharacteristic
342C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2249C2
socleC22×C11C22×D8
hypercenter#2249D11
hypocenterC11#33839
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2249

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. #13080300C2semidirect
3. #13070726C2semidirect
4. #13070668C2semidirect
5. #13070555C2semidirect
6. #13070526C2semidirect
7. C4×D176C2semidirect
8. #13070449C2semidirect
9. C11×#2249C2semidirect
11. C2×D8×D11C22semidirect
13. C2×C11×Q32C22semidirect
14. C2×C11×SD32C22semidirect
16. C11×#495C22semidirect
17. #10622801C22semidirect
18. C2×#66892C22semidirect
26. C2×#66862C22semidirect
27. C4×D88C22semidirect
29. C4×C11×C16C22semidirect
30. #10622202C22semidirect
31. #10622200C22semidirect
32. #10622147C22semidirect
33. (C2×D11)⋊C16C22semidirect
34. #10622142C22semidirect
35. C4⋊(C11⋊C16)C22semidirect
73. D176D4semidirect
120. #2249D11semidirect
161. C2×Q32C2×D11semidirect
163. C2×SD32C2×D11semidirect
168. #495C2×D11semidirect
182. C4×C16C2×D11semidirect
288. C11#33839semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106225272
#130803002
#130707262
#130706682
#130705552
#130705262
C4×D1762
#130704492
C11×#22492
#3383911